hdu 2108 Shape of HDU【判断多边形是否是凸多边形模板】

#include<stdio.h>
#include<math.h>

const int maxn = 100000;
struct Point{
    double x,y;
    Point() {}
    Point(double _x, double _y) {
        x = _x;
        y = _y;
    }

    Point operator -(const Point &B) const {
        return Point(x-B.x, y-B.y);
    }

}p[maxn];

double eps = 1e-10;
int dcmp(double x)
{
    if(fabs(x) < eps) return 0;
    else return x < 0 ? -1 : 1;
}
double Cross(Point A, Point B)
{
    return A.x*B.y - A.y*B.x;
}
/** 判断多边形是否是凸多边形【含共线】*/
bool isConvex(Point *p, int n)
{
    p[n] = p[0]; // 边界处理
    p[n+1] = p[1]; // 注意也可以用 %n 处理, 下标从 0 开始
    int now = dcmp(Cross(p[1]-p[0], p[2]-p[1]));
    for(int i = 1; i < n; i++)
    {
        int next = dcmp(Cross(p[i+1]-p[i], p[i+2]-p[i+1]));
        if(now*next < 0) //此处可以共线
        {
            return false;
        }
        now = next; //注意记录临界条件
    }
    return true;
}
int main()
{
    int n;
    while(scanf("%d", &n) != EOF)
    {
        if(n == 0) break;

        for(int i = 0; i < n; i++)
            scanf("%lf%lf", &p[i].x, &p[i].y);
        bool flag = isConvex(p,n);
        if(flag) printf("convex\n");
        else printf("concave\n");

    }
    return 0;
}